Electron capture branching ratios for the
nuclear matrix elements in double-beta decay
using TITAN
◆
◆
◆
◆
Nuclear matrix elements in double-beta decay.
Present uncertainties
Measurement of electron-capture branching ratios.
A new method using TITAN
D. Frekers, J. Dilling, I. Tanihata
and TITANEC collaboration
TCP06 Parksville 8/5/06
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Double Beta Decay
◆
Two-neutrino decay (2nbb)


◆
This decay is allowed by the standard model and has been observed.
Calculations of the nuclear matrix elements are the main issues to
understanding the decay rates.
Zero-neutrino decay (0nbb)





This mode of decay is forbidden by the standard model.
Requires the neutrino to be a Majorana particle with a mass.
Recent observations of the neutrino oscillation suggest the non-zero mass
of the neutrino and thus this decay mode may exist.
New generation experiments for detecting this mode of decay are in
progress.
Majorana neutrino mass would be determined if this mode of decay is
observed and reliable estimation of the nuclear matrix elements are
available.
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Rate of a 2nbb decay
A
Z A (Z  2) 2e  2ne

2n
G
2n
[Allowed by the standard model]
2n 2
(Q, Z ) M DGT
4


G
where G 2n (Q, Z )  C F cosc  F2 f (Q)
 2


2n 2
M DGT
: Nuclear matrix element

Q: decay Q value

Qc: Cabibbo angle
GF: Fermi coupling constant
F-: Coulomb factor for b- decay
f(Q): phase space factor
C: Relativistic correction
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Nuclear matrix element for 2nbb decays
2n
M DGT

f
k  k  k 1m 1m k  k  k 0igs
0 gs
m
1

Q

E(1
m )  E0
2
M m (GT  )M m (GT  )

Em
m
Gamow-Teller transitions to all
available states.

Fermi-type transitions are negligible
due to the isospin conservation.
.
.
.
.
.
.
1+
1+
1+
1+
0+
i
A(Z+1)
AZ
2nbb
0+
f
A(Z+2)
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Rate of 0nbb decay (Neutrinoless decay)
A


Z A (Z  2) 2e
0n
G
0n
0n
(Q, Z ) M DGT
[Forbidden by the standard model]
gV 0n

M DF
gA
2
mn e

Both Gamow-Teller
and Fermi transitions
are involved.

mn e is theeffective Majorane neutrino mass
= U ei2 mi
i
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Uei: mixing matrix
mi: mass eigenvalues of neutrinos
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Matrix elements of 0nbb decay
0n
M DGT
 f  l k  l k H GT (rlk , Ea ) i
lk
0n
M DF
 f   l k H F (rlk , Ea ) i
lk

Rlk: proton neutron distance in the nucleus
Ea: energy parameter related to the excitation energy
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Theoretical approaches to the matrix elements
◆
Weak-coupling shell model based on G-matrix nucleonnucleon interactions



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W.C Haxton and G.J. Stephenson, Jr., Part. Nucl. Phys 12 (1984) 409.
E. Caurier et al., Phys. Rev. Lett. 77 (1996) 1954.
But not available for all double beta-decay candidates.
Quasiparticle Random phase approximation (QRPA)


J. A. Halbleib and R. A. Solensen, Nucl. Phys. A 98 (1967) 542.
J. Suhonen, Phys. Lett. B 607 (2006) 87.
TCP06 Parksville 8/5/06
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◆
◆
◆
One can test the precession of calculations by comparing
calculations to measured two-neutrino decay rate. The
operator involved in the 2n decay mode is the GamowTeller operator that connects the initial and final states via
virtual transitions to Jp=1+ states in the intermediate
nucleus, only.
The neutrinoless mode, on the other hand connect to all
states in the intermediate nucleus.
For this reason, comparison in 2n is not a direct test of the
precision of the 0n rate calculation, but can be taken as a
necessary condition for the reliability of the calculation.
M. Bhattacharya et al., Phys. Rev. C 58 (1998) 1247.
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Theoretical situation (QRPA)
◆
◆
◆
Both decay modes can be described with ONE parameter, gpp,
that is the particle-particle coupling part of the proton-neutron
two-body interaction.
gpp is fixed by the experimental 2nbb decay half life (gpp~1)
40.0
0nbb decay is insensitive to gpp.
Decomposition of M
GT
30.0
◆
So just trust us!!
Only 1+ is sensitive to gpp
20.0
10.0
However…
0.0
TCP06 Parksville 8/5/06
-10.0
1+ 2+ 3+ 4+ 5+ 6+ 7+ 8+ 0- 1- 2- 3- 4- 5- 6- 7gpp = 0.89
gpp = 1.00 9
gpp = 0.96
gpp = 1.05
116Cd
The case of A=116
J. Suhonen, Phys. Lett. B 607 (2005) 87.
Single state dominance
One can obtain the transition
strength of MEC and Mb
separately.
Exp. EC (direct mea.)
Exp. b-
Exp. EC (3He,t)
M. Bhattacharya et al. Phys. Rev. C 58 (1998) 1247.
H. Akimune et al., Phys. Lett. B 394 (1997) 23.
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Experimental data also show inconsistency
◆
Direct measurement of Electron capture (MEC=0.69)

◆
Extremely small branching compared with b- decay. (~0.023%)
Nucleon transfer reactions (MEC=0.18)

Uncertainty between the proportionality of between B(GT) and the
(3He,t) charge exchange cross section.
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Difficulty in electron capture branching ratio
◆
◆
Measurement should be made by detecting Kx-rays after
capture of electrons under the back ground of x-rays and
grays associated with b- decays.
Neutron activation method,… Reaction with accelerated
beam and tape transport system.




Kx-rays after shake off by electrons.
Bremsstrahlung from electrons.
Beta delayed gamma emission.
Impurity of decay sample.
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A New Method at TITAN
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Observation of x-ray from decays of trapped ions.



No material around the decaying nuclei.
All electrons are swept away by the magnetic field.
No impurity
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ISAC Facility at TRIUMF
TITAN
TCP06 Parksville 8/5/06
M. Bhattacharya et al., PRC 58 (1998)1247.
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TITAN EC
measurement
mode
Mass
measurement
mode
42
3
32
1
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EBIT (Electron Beam Ion Trap)
◆
trap center
◆
6
4
port for X-ray
detector
Use it without the electron gun.
(Penning trap mode)
7 ports for X-ray detection
E-gun
(can be retracted)
B[T]
2
0
-600
-400
-200
0
200
distance from trap center [mm]
400
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100Tc
case as an example
T1/2=15.8 s
◆
Optimization



■
■
■
High detection
efficiency of 17.5 keV
X-rays
Low efficiency for g
rays.
High rejection of eDetector thickness
Be window thickness
Magnetic field
strength
For 1 EC
0.01% branch
beta: 10000
gamma:
44
500
700
TCP06 Parksville 8/5/06
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Simulated spectra (100Tc)
X-ray spectrum by a Si detector (2mm thick)
8x108 decays @0.002% branching ratio with b-ray anticoincidence with 90%
rejection rate.
30
30
25
Counts/0.5keV
B
B
25
20
B
Counts
20
B
15
B
B
10
B
B
B
B
B
B
BB
B
B
B BBB BB
BB
B B BB B
B
B B
BB B
5 BB BBBB B
B
BB
B
BB B B BB
B BB
B B
B
B B
B BB
BB BB B
BBB
BBB B
B
B
BB
B
B B BB BBB B
B
B
B BB B BBB
B BB
B B B B BBB BB
B
BB
B
BBB
B BB BB B
BBBBB
BB BB
B
BB
B BB
BB
B B BB BBB B
BBBB BBB
B
B BBB
BB BBB
B
B BB BB
BB
B
B
B B BB BBBB
BBBB B BB BBB B BB B
BB
B
0
B
B B
0
10
20
30 40 50 60 70
Detected energy [keV]
80
90 100
Counts
Additional background for
1.5x108 decays.
15
10
B
B
B
BB B
BB
B
B
B B
BB B
B
BBB
BBB BBBB BB BB BB
BB
B
BB BB B
B B B
B
BBBB B
B B B
B
BB BBB
B
B
B B
BBBBB
BB B B
BB
B B B B
B
BB
B
BBBBB B
BB B
B
B
BBB BBBBBBBBBB
BBB B
B
B
B
BB BB
BB B BB BB
BBB
BBBB
BBBB BB
BB
BBB
B
B B
BB
B
BBB
B
BBB
0 BBB B BBB BBB B B BBBBBBBBBBB BBBBBBBBBB BB BBBBB BBBBB
5
0
10
20
30 40 50 60 70
Detected energy [keV]
80
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90 100
Simulated spectra (100Tc)
X-ray spectrum by a Si detector (2mm thick)
8x107 decays @0.1% branching ratio and no b-ray anti-coincidence rejection, or
8x108 decays @0.01% branching ratio with b-ray anticoincidence with 90%
rejection rate.
120
B
100
B
Counts/0.5keV
B
Counts
80
60
40
20
BB BB B
B
B
BB
B
BBB
BBBBB BB
B
B
B
BB
BBB
B
B
BBB
B
BBB
B
B
BB
BBB
BBBBB
B
BB
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
BBB
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
BB
BB
BBB
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
BB
BB
0
B
BB
B
0
10
20
30 40 50 60 70
Detected energy [keV]
80
90 100
TCP06 Parksville 8/5/06
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Summary
◆
◆
◆
Radioactive beam facilities and ion traps provides a new possibility for
a precise determination of an extremely small branching ratio of
electron capture.
It will give the best test ground for nuclear models of double beta
decay. It thus provides information on the matrix elements of 0nbb
decays.
Please refer to the paper by D. Frekers, J. Dilling, and I. Tanihata
submitted to publication for detailed discussion of other cases of
double beta decays.
Thank you
TCP06 Parksville 8/5/06
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